共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper is devoted to the problem of estimating the square of population mean (μ2) in normal distribution when a prior estimate or guessed value σ0
2 of the population variance σ2 is available. We have suggested a family of shrinkage estimators , say, for μ2 with its mean squared error formula. A condition is obtained in which the suggested estimator is more efficient than Srivastava et al’s (1980) estimator Tmin. Numerical illustrations have been carried out to demonstrate the merits of the constructed estimator over Tmin. It is observed that some of these estimators offer improvements over Tmin particularly when the population is heterogeneous and σ2 is in the vicinity of σ0
2. 相似文献
2.
Yasuko Chikuse 《Journal of statistical planning and inference》1980,4(4):329-337
The problem of finding confidence regions (CR) for a q-variate vector γ given as the solution of a linear functional relationship (LFR) Λγ = μ is investigated. Here an m-variate vector μ and an m × q matrix Λ = (Λ1, Λ2,…, Λq) are unknown population means of an m(q+1)-variate normal distribution , where ζ′ = (μ′, Λ1′, Λ2′,…, Λq′Σ is an unknown, symmetric and positive definite m × m matrix and Ω is a known, symmetric and positive definite (q+1) × (q+1) matrix and ? denotes the Kronecker product. This problem is a generalization of the univariate special case for the ratio of normal means.A CR for γ with level of confidence 1 ? α, is given by a quadratic inequality, which yields the so-called ‘pseudo’ confidence regions (PCR) valid conditionally in subsets of the parameter space. Our discussion is focused on the ‘bounded pseudo’ confidence region (BPCR) given by the interior of a hyperellipsoid. The two conditions necessary for a BPCR to exist are shown to be the consistency conditions concerning the multivariate LFR. The probability that these conditions hold approaches one under ‘reasonable circumstances’ in many practical situations. Hence, we may have a BPCR with confidence approximately 1 ? α. Some simulation results are presented. 相似文献
3.
Two independent random samples are drawn from two multivariate normal populations with mean vectors μ1 and μ2 and a common
variance-covariance matrix Σ. Ahmed and Saleh (1990) considered preliminary test maximum likelihood estimator (PMLTE) for estimating μ1 based on the Hotelling's T
N
2, when it is suspected that μ1=μ2. In this paper, the PTMLE based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered. Using the quadratic risk function, the conditions of superiority of the proposed estimator for departure
parameter are derived. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated
that the PTMLE based on W test produces the highest minimum guaranteed efficiencies compared to UMLE among the three test procedures. 相似文献
4.
Norbert Henze 《Statistical Papers》2002,43(4):467-506
d -dimensional random vector X is some nondegenerate d-variate normal distribution, on the basis of i.i.d. copies X
1, ..., X
x
of X. Particular emphasis is given to progress that has been achieved during the last decade. Furthermore, we stress the typical
diagnostic pitfall connected with purportedly ‘directed’ procedures, such as tests based on measures of multivariate skewness.
Received: April 30, 2001; revised version: October 30, 2001 相似文献
5.
6.
We consider the situation where one wants to maximise a functionf(θ,x) with respect tox, with θ unknown and estimated from observationsy
k
. This may correspond to the case of a regression model, where one observesy
k
=f(θ,x
k
)+ε
k
, with ε
k
some random error, or to the Bernoulli case wherey
k
∈{0, 1}, with Pr[y
k
=1|θ,x
k
|=f(θ,x
k
). Special attention is given to sequences given by
, with
an estimated value of θ obtained from (x1, y1),...,(x
k
,y
k
) andd
k
(x) a penalty for poor estimation. Approximately optimal rules are suggested in the linear regression case with a finite horizon,
where one wants to maximize ∑
i=1
N
w
i
f(θ, x
i
) with {w
i
} a weighting sequence. Various examples are presented, with a comparison with a Polya urn design and an up-and-down method
for a binary response problem. 相似文献
7.
Summary The Zenga index,
, is shown to be a concentration index, in the sense that, ifX andY are non negative random variables with 0<E(X), E(Y)<+∞, then
(X)⩾
(Y) whenever the Lorenz curves satisfyL
x(p)≤L
y(p) for all p.
Research partially supported by: M.U.R.S.T. 40% ?Inferenza statistica: basi probabilistiche e sviluppi metodologici?. 相似文献
8.
Mohamed Hebiri 《Statistics and Computing》2010,20(2):253-266
Conformal predictors, introduced by Vovk et al. (Algorithmic Learning in a Random World, Springer, New York, 2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed
data. We propose a novel method for constructing prediction intervals for the response variable in multivariate linear models.
The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response
variable even if the total number of covariates is very large. Our approach is based on combining the principle of conformal
prediction with the ℓ
1 penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter ε>0 and has a coverage probability larger than or equal to 1−ε. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product
of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method
is illustrated on simulated and real data. 相似文献
9.
A. Stepanov 《Statistical Papers》2007,48(1):63-79
LetX
1,X
2, … be a sequence of i.i.d. random variables with some continuous distribution functionF. LetX(n) be then-th record value associated with this sequence and μ
n
−
, μ
n
+
be the variables that count the number of record values belonging to the random intervals(f−(X(n)), X(n)), (X(n), f+(X(n))), wheref−, f+ are two continuous functions satisfyingf−(x)<x, f+(x)>x. Properties of μ
n
−
, μ
n
+
are studied in the present paper. Some statistical applications connected with these variables are also provided. 相似文献
10.
Ricardo Aníbal Leiva 《Statistical Methods and Applications》1994,3(2):271-289
Summary The problem of predicting the number of change points in a piecewise linear model is studied from a Bayesian viewpoint. For
a given a priori joint probability functionf
R,C=fRf
C/R, whereR is the number of change points andC=C′(R)=(C1,…,CR) is the change-point epoch vector, the marginal posterior probability functionf
R.C/Y
is obtained, and then used to find predictors forR andC(R). 相似文献
11.
Suppose the p -variate random vector W , partitioned into q variables W1 and p - q variables W2 , follows a multivariate normal mixture distribution. If the investigator is mainly interested in estimation of the parameters of the distribution of W1 , there are two possibilities: (1) use only the data on W1 for estimation, and (2) estimate the parameters of the p -variate mixture distribution, and then extract the estimates of the marginal distribution of W1 . In this article we study the choice between these two possibilities mainly for the case of two mixture components with identical covariance matrices. We find the asymptotic distribution of the linear discriminant function coefficients using the work of Efron (1975 ) and O'Neill (1978 ), and give a Wald–test for redundancy of W2 . A simulation study gives further insights into conditions under which W2 should be used in the analysis: in summary, the inclusion of W2 seems justified if Δ 2.1, the Mahalanobis distance between the two component distributions based on the conditional distribution of W2 given W1 , is at least 2. 相似文献
12.
This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVARS(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix. 相似文献
13.
Estimation of a normal mean relative to balanced loss functions 总被引:3,自引:0,他引:3
LetX
1,…,X
nbe a random sample from a normal distribution with mean θ and variance σ2. The problem is to estimate θ with Zellner's (1994) balanced loss function,
% MathType!End!2!1!, where 0<ω<1. It is shown that the sample mean
% MathType!End!2!1!, is admissible. More generally, we investigate the admissibility of estimators of the form
% MathType!End!2!1! under
% MathType!End!2!1!. We also consider the weighted balanced loss function,
% MathType!End!2!1!, whereq(θ) is any positive function of θ, and the class of admissible linear estimators is obtained under such loss withq(θ) =e
θ
. 相似文献
14.
ELISA M. MOLANES LOPEZ INGRID VAN KEILEGOM NOËL VERAVERBEKE 《Scandinavian Journal of Statistics》2009,36(3):413-432
Abstract. Suppose that X 1 ,…, X n is a sequence of independent random vectors, identically distributed as a d -dimensional random vector X . Let be a parameter of interest and be some nuisance parameter. The unknown, true parameters ( μ 0 , ν 0 ) are uniquely determined by the system of equations E { g ( X , μ 0 , ν 0 )} = 0 , where g = ( g 1 ,…, g p + q ) is a vector of p + q functions. In this paper we develop an empirical likelihood (EL) method to do inference for the parameter μ 0 . The results in this paper are valid under very mild conditions on the vector of criterion functions g . In particular, we do not require that g 1 ,…, g p + q are smooth in μ or ν . This offers the advantage that the criterion function may involve indicators, which are encountered when considering, e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed EL method for small samples. 相似文献
15.
Consider the problem of obtaining a confidence interval for some function g(θ) of an unknown parameter θ, for which a (1-α)-confidence
interval is given. If g(θ) is one-to-one the solution is immediate. However, if g is not one-to-one the problem is more complex
and depends on the structure of g. In this note the situation where g is a nonmonotone convex function is considered. Based
on some inequality, a confidence interval for g(θ) with confidence level at least 1-α is obtained from the given (1-α) confidence
interval on θ. Such a result is then applied to the n(μ, σ
2) distribution with σ known. It is shown that the coverage probability of the resulting confidence interval, while being greater
than 1-α, has in addition an upper bound which does not exceed Θ(3z1−α/2)-α/2. 相似文献
16.
Let σ1 , …, σk be the covariance matrices of k p -variate normal populations. Let Λij be the j th largest characteristic root of σi (j=1, …, p; i=1, …, k). In this note we obtain simultaneous confidence intervals on (i)Λi+1, p /Λip and by using methods similar to those of Khatri (1965). 相似文献
17.
David D. Hanagal 《Statistical Papers》1999,40(1):99-106
In this paper, we estimate the reliability of a system with k components. The system functions when at least s (1≤s≤k) components survive a common random stress. We assume that the strengths of these k components are subjected to a common
stress which is independent of the strengths of these k components. If (X
1,X
2,…,X
k
) are strengths of k components subjected to a common stress (Y), then the reliability of the system or system reliability
is given byR=P[Y<X
(k−s+1)] whereX
(k−s+1) is (k−s+1)-th order statistic of (X
1,…,X
k
). We estimate R when (X
1,…,X
k
) follow an absolutely continuous multivariate exponential (ACMVE) distribution of Hanagal (1993) which is the submodel of
Block (1975) and Y follows an independent exponential distribution. We also obtain the asymptotic normal (AN) distribution
of the proposed estimator. 相似文献
18.
Two variance components model for which each invariant quadratic admissible estimator of a linear function of variance components
(under quadratic loss function) is a linear combination of two quadratic forms,Z
1,Z
2, say, is considered. A setD={(d
1,d
2)′:d
1
Z
1+d
2
Z
2 is admissible} is described by giving formulae on the boundary ofD. Different forms of the setD are presented on figures. 相似文献
19.
Let X1, …,Xn, and Y1, … Yn be consecutive samples from a distribution function F which itself is randomly chosen according to the Ferguson (1973) Dirichlet-process prior distribution on the space of distribution functions. Typically, prediction intervals employ the observations X1,…, Xn in the first sample in order to predict a specified function of the future sample Y1, …, Yn. Here one- and two-sided prediction intervals for at least q of N future observations are developed for the situation in which, in addition to the previous sample, there is prior information available. The information is specified via the parameter α of the Dirichlet process prior distribution. 相似文献
20.
Michael Falk 《统计学通讯:理论与方法》2013,42(7):1729-1755
Consider n independent random variables Zi,…, Zn on R with common distribution function F, whose upper tail belongs to a parametric family F(t) = Fθ(t),t ≥ x0, where θ ∈ ? ? R d. A necessary and sufficient condition for the family Fθ, θ ∈ ?, is established such that the k-th largest order statistic Zn?k+1:n alone constitutes the central sequence yielding local asymptotic normality ( LAN ) of the loglikelihood ratio of the vector (Zn?i+1:n)1 i=kof the k largest order statistics. This is achieved for k = k(n)→n→∞∞ with k/n→n→∞ 0. In the case of vectors of central order statistics ( Zr:n, Zr+1:n,…, Zs:n ), with r/n and s/n both converging to q ∈ ( 0,1 ), it turns out that under fairly general conditions any order statistic Zm:n with r ≤ m ≤s builds the central sequence in a pertaining LAN expansion.These results lead to asymptotically optimal tests and estimators of the underlying parameter, which depend on single order statistics only 相似文献